Evaluating Phonon Characteristics by Varying the Layer and Interfacial Thickness in Novel Carbon-Based Strained-Layer Superlattices

Abstract

Systematic results of lattice dynamical calculations are reported as a function of m and n for the novel (SiC)_m/(GeC)_n superlattices (SLs) by exploiting a modified linear-chain model and a realistic rigid-ion model (RIM). A bond polarizability method is employed to simulate the Raman intensity profiles (RIPs) for both the ideal and graded (SiC)_10-&Delta;/(Si_0.5Ge_0.5C)_&Delta;/(GeC)_10-&Delta;/(Si_0.5Ge_0.5C)_&Delta; SLs. We have adopted a virtual-crystal approximation for describing the interfacial layer thickness, &Delta; (&equiv;0, 1, 2, and 3 monolayers (MLs)) by selecting equal proportions of SiC and GeC layers. Systematic variation of &Delta; has initiated considerable upward (downward) shifts of GeC-(SiC)-like Raman peaks in the optical phonon frequency regions. Our simulated results of RIPs in SiC/GeC SLs are agreed reasonably well with the recent analyses of Raman scattering data on graded short-period GaN/AlN SLs. Maximum changes in the calculated optical phonons (up to &plusmn;~47 cm^&minus;1) with &Delta; = 3, are proven effective for causing accidental degeneracies and instigating localization of atomic displacements at the transition regions of the SLs. Strong &Delta;-dependent enhancement of Raman intensity features in SiC/GeC are considered valuable for validating the interfacial constituents in other technologically important heterostructures. By incorporating RIM, we have also studied the phonon dispersions [<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><msubsup><mrow><msub><mrow><mi mathvariant="sans-serif">&omega;</mi></mrow><mrow></mrow></msub></mrow><mrow><mi mathvariant="normal">j</mi></mrow><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">L</mi></mrow></msubsup></mrow><mrow></mrow></msub><mfenced separators="|"><mrow><mover accent="true"><mrow><mi mathvariant="bold">q</mi></mrow><mo>&rarr;</mo></mover></mrow></mfenced></mrow></semantics></math></inline-formula>] of (SiC)_m/(GeC)_n SLs along the growth [001] as well as in-plane [100], [110] directions [i.e., perpendicular to the growth]. In the acoustic mode regions, our results of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><msubsup><mrow><msub><mrow><mi mathvariant="sans-serif">&omega;</mi></mrow><mrow></mrow></msub></mrow><mrow><mi mathvariant="normal">j</mi></mrow><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">L</mi></mrow></msubsup></mrow><mrow></mrow></msub><mfenced separators="|"><mrow><mover accent="true"><mrow><mi mathvariant="bold">q</mi></mrow><mo>&rarr;</mo></mover></mrow></mfenced><mo>&nbsp;</mo></mrow></semantics></math></inline-formula> have confirmed the formation of mini-gaps at the zone center and zone edges while providing strong evidences of the anti-crossing and phonon confinements. Besides examining the angular dependence of zone-center optical modes, the results of phonon folding, confinement, and anisotropic behavior in (SiC)_m/(GeC)_n are compared and contrasted very well with the recent first-principles calculations of (GaN)_m/(AlN)_n strained layer SLs.